This study analyzes failure modes in distal femoral implants through biomechanical modeling. For the distal region, beam theory shows strain in bone decreases as the blade width increases, with rectangular cross-sections causing most strain. Proximally, a longer plate reduces screw force by 30% and more gradually distributes stress, though clamping length did not strongly affect peak bone stress. An optimal design would combine features of blade plates and fixed angle plates.

1. STUDY OF FAILURE MODES IN DISTAL FEMORAL IMPLANTS
PIERRE CHESNOT
DECEMBER 12, 2015

2. INTRODUCTION
Distal femoral fixation plates are commonly used to repair severe fractures of the femur. These
fractures are common in older people with low bone density, athletes, or in traumatic injuries. In
their “Biomechanical Analysis of Distal Femur Fracture Fixation,” Higgins et al. concluded
through experimental destructive testing that Condylar Blade Plates (CBP) were more resistant
than Fixed Angle Fixation Plates (FAFP). In their experiment, they attached the plates, redrawn
in Figure 1, to the distal end of cadaver femurs and osteotomized a 1 cm gap just above the
condyles to simulate a gap fracture and force any load applied to be transferred fully to the
fixation plate. They then potted the proximal end of the femurs and applied a compressive load
evenly to the condylar surface. On average, the FAFP failed at loads 62% higher than the CBP.
However, the interesting part is the modes of failure. The CBP unanimously failed on the
proximal side of the gap, while the FAFP failed in the condylar region on the distal side. In both
cases, the failure came not from the metal yielding, but rather from the screws cutting through
the bone.
In my own study, I analyze both the distal and the
proximal failure modes using Beam on Elastic
Foundation (BOEF) theory to compute strain and
stress in the bone. In the distal region, since the
blade plate clearly performed better due to its wide
profile penetrating the bone, I look at the effect of
changing the width and the shape of that blade. In
the proximal region, I investigate how the clamping
length affects stress in the screws, but also in the
underlying bone. From these analyses, I hope to
come up with an optimal fixation device strategy.
DISTAL BIOMECHANICAL ANALYSIS
In the first part of this problem, the failure mechanism in the distal part of the femur was
analyzed. The paper that was reviewed states that failure of the FAFP happened in this region,
with the screws cutting through the bone. However, this did not happen with the CBP, where the
blade has a much wider profile than the screws of the FAFP. To analyze this phenomenon, I
decided to compare the stress in the bone due to changing profiles of the implant in that region,
and therefore isolated that area and simplified the problem to a force acting on the implant, with
Figure
1
–
LEFT:
Condylar
Blade
Plate
(CBP).
RIGHT:
Fixed
Angle
Fixation
Plate
(FAFP).

3. bone surrounding it. This is shown in the free
body diagrams in Figure 2. BOEF analysis was
conducted on the model using the constants in
Table 1. The stiffness of the bone, moment of
area of the implant cross-section, and λ of the
system were calculated using the following
equations:
𝑘 =
!!!
!
, 𝐼! =
!!!
!"
𝑜𝑟
!
!"
𝑑!
, 𝜆 =
!
!!!!!
!
!
The deflection was then computed per the
following formula (Bartel 2006:208):
𝑣 =
𝑃𝜆
𝑘
1
sinh! 𝜆𝑙 − sin! 𝜆𝑙
{2 cosh 𝜆𝑥 cos 𝜆𝑥 sinh 𝜆𝑙 cos 𝜆𝑎 cosh 𝜆𝑏 − sin 𝜆𝑙 cosh 𝜆𝑎 cosh 𝜆𝑏
+ cosh 𝜆𝑥 sin 𝜆𝑥 + sinh 𝜆𝑥 cos 𝜆𝑥 sinh 𝜆𝑙 sin 𝜆𝑎 cosh 𝜆𝑏 − cos 𝜆𝑎 sinh 𝜆𝑏
+ sin 𝜆𝑙 sinh 𝜆𝑎 cos 𝜆𝑏 − cosh 𝜆𝑎 sin 𝜆𝑏 }
Finally, the strain at the interface was obtained using this deflection in the equation: 𝜀 =
!
!
.
By varying the width of the blade section and computing the max strain (right under the load)
each time, I obtained the blue line in Figure 3, clearly showing that the bone strain at the
interface with the implant decreases greatly as the implant is widened. I then compared this max
strain to purely circular and square cross-sections by altering the moments of area. As can be
seen in Figure 3, the bone strain at the interface is greatest for a rectangular cross section, and
slightly lower for a square section than a circular section.
4 6 8 10 12 14 16 18 20
Width of Implant (mm)
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Strain
Strain in Bone
Rectangular
Square
Circular
Figure
3
–
Max
strain
in
bone
as
result
of
load
P.
Figure
2
–
TOP:
Free
body
diagram
of
condylar
blade.
BOTTOM:
Simplified
model
for
BOEF
analysis.
Symbol Value Description
𝑙 60 mm Length of blade
d 35 mm Distance to center of
condylar head
H 40 mm Bone effective height
h 4.5 mm Thickness of blade
ES 195,000 MPa Modulus of screws
DS 4.5 mm Diameter of screw
AS 15.9 mm2
Area of single screw
LS 30 mm Length of screw
L 200 mm;
150 mm
Clamping lengths
EP 195,000 MPa Modulus of plate
Eb 500 MPa Modulus of bone
Ab 908 mm2
Area of bone
s 17 mm Distance to max stress
Table
1
–
Constants
used
throughout
analysis.

4. PROXIMAL ANALYSIS
Once I had an idea of the effect of blade geometry on
the strain of the surrounding bone, I decided to shift
my focus to the proximal side of the fracture. In this
area, I wanted to see if the clamping length of the
implant had an effect on bone stress and possible
fracture, but also to learn about the stress distribution
in the screws.
In order to tackle this problem, I isolated the proximal part of the fixation devices. Since there
was the same number of screws, the only difference between both devices was the plate length.
I then chose to model this system as two beams (plate and bone) separated by an elastic
foundation (screws), as shown in Figure 3. However, the stiffness of the elastic foundation
became a problem, because it was not bone cement as represented by the quantity Ct (Bartel
2006:211). Instead, I chose to relate it to the material stiffness of a screw, but also to the length
over which the screws were fastened. Because of this, I decided to add a ratio of length taken
up by screws to total clamping length as a weight factor to the usual material stiffness equation
and calculated Ct using the constants in Table 1 and the following equation:
𝐶! =
𝐸! 𝐴!
𝐿!
4 ∗ 𝐷!
𝐿
While this may not return exactly accurate numerical values, it should allow for a comparison of
the force exerted by the elastic foundation (screws) for different clamping lengths L. I then
calculated λt in order to compute the force per unit length q exerted by the foundation:
𝜆! =
𝐶!
4
1
𝐸! 𝐼!
+
1
𝐸! 𝐼!
!
!
𝑞 = 𝑀
1
2
𝐶!
𝜆!
! 𝐸! 𝐼! 𝑒!!!!
(cos 𝜆! 𝑥 + sin 𝜆! 𝑥)
This force is shown in Figure 5, and is initially reduced by approximately 30% for the FAFP as
opposed to the CBP. While this gave me an idea of the stress distribution in the 4 screws, I was
also concerned about the bending stress in the bone. Therefore, using the following equations, I
calculated the bending moment in the bone and the maximum compressive stress in the bone
as a result of both this moment and the axial load P exerted on the plate.
𝑀! = 𝑀
𝐸! 𝐼!
𝐸! 𝐼! + 𝐸! 𝐼!
𝐸! 𝐼!
𝐸! 𝐼!
+ 𝑒!!!!
cos 𝜆! 𝑥 + sin 𝜆! 𝑥
Figure
4
–
Max
strain
in
bone
as
result
of
load
P.

5. 𝜎!"#,!"#$ =
𝑀! 𝑠
𝐼!
+
𝑃
𝐴!
This stress, shown in Figure 6, reached the same magnitude of 8.2 MPa at the start of the
interface, regardless of plate length. However, the longer plate (FAFP) caused a more gradual
decline of this stress and lower slope of the curve.
DISCUSSION
According to my analysis, the ideal fracture fixation plate would be a hybrid design pulling from
both the CBP and the FAFP that were studied. It is clear that inclusion of a blade is beneficial,
since those specimens never broke in the distal region in the experiments conducted by Higgins
et al. In fact, widening this blade drastically decreases the strain and stress in the surrounding
bone. Looking at the blue line in Figure 3, we can see that the strain is decreased 3-fold from
over 3% to about 1% by increasing the width of the blade from 4 to 12 mm. This is valuable
information, as we can optimize blade widths to ensure bone stresses will stay below the
strength threshold of trabecular bone. The more interesting information came from exploring the
possibility of changing the shape of the blade cross-section. The red line in Figure 3 represents
a growing square cross-section, while the yellow one represents a growing circular cross-
section. As these two shapes grow, their area increases exponentially and they take up much
more room in the bone than the rectangle with constant height represented by the blue line.
However, at equivalent width, they only decrease the bone strain by 0.2%, which is not worth
the extra volume it would take up in the bone.
0 20 40 60 80 100 120 140 160 180 200
Distance from Fracture (mm)
-2
0
2
4
6
8
10
12
14
16
Force(N)
#10
6 Foundation Force per Length (Screws)
Long Plate (FAFP)
Short Plate (CBP)
0 20 40 60 80 100 120 140 160 180 200
Distance from Fracture (mm)
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
Stress(Pa)
#106 Max Bending Stress in Bone
Long Plate (FAFP)
Short Plate (CBP)
Figure
5
–
Distribution
of
Force
in
Elastic
Foundation
(Screws)
Figure
6
–
Max
Compressive
Bending
Stress
in
Bone.

6. On the proximal side of the implant, clamping length did not seem to have the drastic effect
Higgins et al. expected on the bone stress at the interface. In their paper, they state that
“Perhaps the shaft fixation of the blade plate could have withstood greater loading if the
proximal fixation had been spread out farther over a longer plate segment.” (Higgins 2006:4). In
fact, in both clamping lengths analyzed, stress in the bone started at the same value of around
8.2 MPa and decreased down the length of the fixation plate. However, the shorter fixation
length (CBP) did cause a slightly steeper reduction in stress. Although unlikely, it is possible that
this narrower stress peak created a more acute stress gradient in the trabecular bone and
caused it to fracture.
While the clamping length’s effect on bone stress remains questionable, it clearly did reduce the
force exerted by the screws, modeled by an elastic foundation. The longer fixation device
(FAFP) caused this force to be 30% lower than in the shorter plate (CBP), but also less steep
and therefore spread out over a greater distance. In our case, this would represent a more
evenly distributed load sharing between all four screws. Both these conclusions would point our
design to encouraging longer clamping length.
In the distal analysis, there are obvious limits to the size the blade of the implant can reach, in
order for this device to fit within the condylar head of the femur. Also, while the analysis
conducted was limited to vertical compression, in reality the blade of the implant would
experience torsion and moments in other directions. Therefore, the thin shape of the cross-
section might have adverse effects in those directions.
Proximally, the limitations of the analysis are clear. The screws of the fixation devices were
modeled as an elastic foundation, but in reality they do not make a continuous interface
between the bone and the implant. This means that using their material stiffness as the input Ct
gives us, at best, an approximation. A better approach might be to determine this stiffness
experimentally by loading a model system and obtaining actual deflection values using strain
gauges.
REFERENCES
1. Higgins, T., Pittman, G., Hines, J., & Bachus, K. (2006). Biomechanical Analysis of Distal
Femur Fracture Fixation: Fixed-Angle Screw-Plate Construct Versus Condylar Blade
Plate. Journal of Orthopaedic Trauma, 43-46.
2. Bartel, D., Davy, D., & Keaveny, T. (2006). Orthopaedic biomechanics: Mechanics and
design in musculoskeletal systems. Upper Saddle River, N.J.: Pearson/Prentice Hall,
208-213.